Results 11 to 20 of about 6,408 (248)
Commuting planar polynomial vector fields for conservative newton systems [PDF]
ACM Communications in Computer Algebra, 2019 We study the problem of characterizing polynomial vector fields that commute with a given polynomial vector field on a plane. It is a classical result that one can write down solution formulas for an ODE that corresponds to a planar vector field that possesses a linearly independent (transversal) commuting vector field (see Theorem 2.1 ...
Joel Nagloo +2 more
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Deciding reachability for planar multi-polynomial systems [PDF]
, 1996 In this paper we investigate the decidability of the reachability problem for planar non-linear hybrid systems. A planar hybrid system has the property that its state space corresponds to the standard Euclidean plane, which is partitioned into a finite number of (polyhedral) regions.
Karlis Cerans, Juris Viksna
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ON THE GLOBAL CENTER OF PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS AND THE RELATED PROBLEMS
Journal of Applied Analysis & Computation, 2022 Summary: In the paper we characterize planar polynomial differential systems with a global center, that is, every orbit of the system is a periodic orbit in \(\mathbb{R}^2\). Further, we give algebraic sufficient and necessary conditions for potential systems and Liénard systems which have a global center, respectively.
He, Hongjin, Xiao, Dongmei
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European Journal of Remote Sensing, 2023 The GaoFen-14 (GF-14) satellite is China’s most recent high-resolution earth observation satellite system. It is equipped with a two linear-array stereo camera and is intend for topographic mapping at 1:10,000-scale without ground control points (GCPs ...
Bincai Cao +8 more
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Application of Power Geometry and Normal Form Methods to the Study of Nonlinear ODEs
EPJ Web of Conferences, 2018 This paper describes power transformations of degenerate autonomous polynomial systems of ordinary differential equations which reduce such systems to a non-degenerative form.
Edneral Victor
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Sensors, 2017 We present in this paper a polynomial fitting method applicable to segments of footprints measured by the Geoscience Laser Altimeter System (GLAS) to estimate glacier thickness change.
Tianjin Huang +5 more
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Automatic Planar Optical Waveguide Devices Packaging System Based on Polynomial Fitting Algorithm
Advances in Mechanical Engineering, 2013 This paper has proposed an automatic precise alignment coupling algorithm of planar optical waveguide devices based on polynomial fitting, and the experiment shows that for 1 × 8 planar optical waveguide splitter, the time it takes for alignment is ...
Yu Zheng +3 more
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Results in Physics, 2022 The coupled nonlinear Maccari systems are very important equations which have been developed vigorously in the fields of the nonlinear optics, deep water theory, plasma physics, nonlinear optics and so on.
Zhao Li, Xinyu Xie, Changjiang Jin
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Isochronicity conditions for some planar polynomial systems II
Bulletin des Sciences Mathématiques, 2011 We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $$\dot x=-y+A(x,y),\;\dot y=x+B(x,y),$$ where $A,\;B\in \mathbb{R}[x,y]$, which can be reduced to the Liénard type equation. When $deg(A)\leq 4$ and $deg(B) \leq 4$, using the so-called C-algorithm we found $36$ new families of isochronous centers. When the Urabe function $h=0$ we
Bardet, Magali +3 more
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Polynomial and rational first integrals for planar homogeneous polynomial differential systems [PDF]
Publicacions Matemàtiques, 2014 In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic homogeneous polynomial differential systems.
Giné, Jaume, Grau, Maite, Llibre, Jaume
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